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<a href="#nested-classes">Classes</a> &#124;
<a href="#func-members">Functions</a>  </div>
  <div class="headertitle">
<div class="title">Spline and spline fitting module<div class="ingroups"><a class="elRef" href="../group__Geometry__chapter.html">Geometry</a> &raquo; <a class="elRef" href="../group__Geometry__Reference.html">Reference</a></div></div>  </div>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<p>This module provides a simple multi-dimensional spline class while offering most basic functionality to fit a spline to point sets.</p>
<div class="fragment"><div class="line"><span class="preprocessor">#include &lt;unsupported/Eigen/Splines&gt;</span></div>
</div><!-- fragment --> <table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="nested-classes"></a>
Classes</h2></td></tr>
<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1Spline.html">Eigen::Spline&lt; Scalar_, Dim_, Degree_ &gt;</a></td></tr>
<tr class="memdesc:"><td class="mdescLeft">&#160;</td><td class="mdescRight">A class representing multi-dimensional spline curves.  <a href="classEigen_1_1Spline.html#details">More...</a><br /></td></tr>
<tr class="separator:"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">struct &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="structEigen_1_1SplineFitting.html">Eigen::SplineFitting&lt; SplineType &gt;</a></td></tr>
<tr class="memdesc:"><td class="mdescLeft">&#160;</td><td class="mdescRight"><a class="el" href="classEigen_1_1Spline.html" title="A class representing multi-dimensional spline curves.">Spline</a> fitting methods.  <a href="structEigen_1_1SplineFitting.html#details">More...</a><br /></td></tr>
<tr class="separator:"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">struct &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="structEigen_1_1SplineTraits_3_01Spline_3_01Scalar___00_01Dim___00_01Degree___01_4_00_01__DerivativeOrder_01_4.html">Eigen::SplineTraits&lt; Spline&lt; Scalar_, Dim_, Degree_ &gt;, _DerivativeOrder &gt;</a></td></tr>
<tr class="memdesc:"><td class="mdescLeft">&#160;</td><td class="mdescRight">Compile-time attributes of the <a class="el" href="classEigen_1_1Spline.html" title="A class representing multi-dimensional spline curves.">Spline</a> class for fixed degree.  <a href="structEigen_1_1SplineTraits_3_01Spline_3_01Scalar___00_01Dim___00_01Degree___01_4_00_01__DerivativeOrder_01_4.html#details">More...</a><br /></td></tr>
<tr class="separator:"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">struct &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="structEigen_1_1SplineTraits_3_01Spline_3_01Scalar___00_01Dim___00_01Degree___01_4_00_01Dynamic_01_4.html">Eigen::SplineTraits&lt; Spline&lt; Scalar_, Dim_, Degree_ &gt;, Dynamic &gt;</a></td></tr>
<tr class="memdesc:"><td class="mdescLeft">&#160;</td><td class="mdescRight">Compile-time attributes of the <a class="el" href="classEigen_1_1Spline.html" title="A class representing multi-dimensional spline curves.">Spline</a> class for Dynamic degree.  <a href="structEigen_1_1SplineTraits_3_01Spline_3_01Scalar___00_01Dim___00_01Degree___01_4_00_01Dynamic_01_4.html#details">More...</a><br /></td></tr>
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</table><table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
Functions</h2></td></tr>
<tr class="memitem:ga1b4cbde5d98411405871accf877552d2"><td class="memTemplParams" colspan="2">template&lt;typename PointArrayType , typename KnotVectorType &gt; </td></tr>
<tr class="memitem:ga1b4cbde5d98411405871accf877552d2"><td class="memTemplItemLeft" align="right" valign="top">void&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="group__Splines__Module.html#ga1b4cbde5d98411405871accf877552d2">Eigen::ChordLengths</a> (const PointArrayType &amp;pts, KnotVectorType &amp;chord_lengths)</td></tr>
<tr class="memdesc:ga1b4cbde5d98411405871accf877552d2"><td class="mdescLeft">&#160;</td><td class="mdescRight">Computes chord length parameters which are required for spline interpolation.  <a href="group__Splines__Module.html#ga1b4cbde5d98411405871accf877552d2">More...</a><br /></td></tr>
<tr class="separator:ga1b4cbde5d98411405871accf877552d2"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ga9474da5ed68bbd9a6788a999330416d6"><td class="memTemplParams" colspan="2">template&lt;typename KnotVectorType &gt; </td></tr>
<tr class="memitem:ga9474da5ed68bbd9a6788a999330416d6"><td class="memTemplItemLeft" align="right" valign="top">void&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="group__Splines__Module.html#ga9474da5ed68bbd9a6788a999330416d6">Eigen::KnotAveraging</a> (const KnotVectorType &amp;parameters, DenseIndex degree, KnotVectorType &amp;knots)</td></tr>
<tr class="memdesc:ga9474da5ed68bbd9a6788a999330416d6"><td class="mdescLeft">&#160;</td><td class="mdescRight">Computes knot averages.  <a href="group__Splines__Module.html#ga9474da5ed68bbd9a6788a999330416d6">More...</a><br /></td></tr>
<tr class="separator:ga9474da5ed68bbd9a6788a999330416d6"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:gae10a6f9b6ab7fb400a2526b6382c533b"><td class="memTemplParams" colspan="2">template&lt;typename KnotVectorType , typename ParameterVectorType , typename IndexArray &gt; </td></tr>
<tr class="memitem:gae10a6f9b6ab7fb400a2526b6382c533b"><td class="memTemplItemLeft" align="right" valign="top">void&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="group__Splines__Module.html#gae10a6f9b6ab7fb400a2526b6382c533b">Eigen::KnotAveragingWithDerivatives</a> (const ParameterVectorType &amp;parameters, const unsigned int degree, const IndexArray &amp;derivativeIndices, KnotVectorType &amp;knots)</td></tr>
<tr class="memdesc:gae10a6f9b6ab7fb400a2526b6382c533b"><td class="mdescLeft">&#160;</td><td class="mdescRight">Computes knot averages when derivative constraints are present. Note that this is a technical interpretation of the referenced article since the algorithm contained therein is incorrect as written.  <a href="group__Splines__Module.html#gae10a6f9b6ab7fb400a2526b6382c533b">More...</a><br /></td></tr>
<tr class="separator:gae10a6f9b6ab7fb400a2526b6382c533b"><td class="memSeparator" colspan="2">&#160;</td></tr>
</table>
<h2 class="groupheader">Function Documentation</h2>
<a id="ga1b4cbde5d98411405871accf877552d2"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ga1b4cbde5d98411405871accf877552d2">&#9670;&nbsp;</a></span>ChordLengths()</h2>

<div class="memitem">
<div class="memproto">
<div class="memtemplate">
template&lt;typename PointArrayType , typename KnotVectorType &gt; </div>
      <table class="memname">
        <tr>
          <td class="memname">void Eigen::ChordLengths </td>
          <td>(</td>
          <td class="paramtype">const PointArrayType &amp;&#160;</td>
          <td class="paramname"><em>pts</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">KnotVectorType &amp;&#160;</td>
          <td class="paramname"><em>chord_lengths</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
      </table>
</div><div class="memdoc">

<p>Computes chord length parameters which are required for spline interpolation. </p>
<dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramdir">[in]</td><td class="paramname">pts</td><td>The data points to which a spline should be fit. </td></tr>
    <tr><td class="paramdir">[out]</td><td class="paramname">chord_lengths</td><td>The resulting chord length vector.</td></tr>
  </table>
  </dd>
</dl>
<dl class="section see"><dt>See also</dt><dd>Les Piegl and Wayne Tiller, The NURBS book (2nd ed.), 1997, 9.2.1 Global Curve Interpolation to Point Data </dd></dl>

</div>
</div>
<a id="ga9474da5ed68bbd9a6788a999330416d6"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ga9474da5ed68bbd9a6788a999330416d6">&#9670;&nbsp;</a></span>KnotAveraging()</h2>

<div class="memitem">
<div class="memproto">
<div class="memtemplate">
template&lt;typename KnotVectorType &gt; </div>
      <table class="memname">
        <tr>
          <td class="memname">void Eigen::KnotAveraging </td>
          <td>(</td>
          <td class="paramtype">const KnotVectorType &amp;&#160;</td>
          <td class="paramname"><em>parameters</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">DenseIndex&#160;</td>
          <td class="paramname"><em>degree</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">KnotVectorType &amp;&#160;</td>
          <td class="paramname"><em>knots</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
      </table>
</div><div class="memdoc">

<p>Computes knot averages. </p>
<p>The knots are computed as </p><p class="formulaDsp">
\begin{align*} u_0 &amp; = \hdots = u_p = 0 \\ u_{m-p} &amp; = \hdots = u_{m} = 1 \\ u_{j+p} &amp; = \frac{1}{p}\sum_{i=j}^{j+p-1}\bar{u}_i \quad\quad j=1,\hdots,n-p \end{align*}
</p>
<p> where \(p\) is the degree and \(m+1\) the number knots of the desired interpolating spline.</p>
<dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramdir">[in]</td><td class="paramname">parameters</td><td>The input parameters. During interpolation one for each data point. </td></tr>
    <tr><td class="paramdir">[in]</td><td class="paramname">degree</td><td>The spline degree which is used during the interpolation. </td></tr>
    <tr><td class="paramdir">[out]</td><td class="paramname">knots</td><td>The output knot vector.</td></tr>
  </table>
  </dd>
</dl>
<dl class="section see"><dt>See also</dt><dd>Les Piegl and Wayne Tiller, The NURBS book (2nd ed.), 1997, 9.2.1 Global Curve Interpolation to Point Data </dd></dl>

</div>
</div>
<a id="gae10a6f9b6ab7fb400a2526b6382c533b"></a>
<h2 class="memtitle"><span class="permalink"><a href="#gae10a6f9b6ab7fb400a2526b6382c533b">&#9670;&nbsp;</a></span>KnotAveragingWithDerivatives()</h2>

<div class="memitem">
<div class="memproto">
<div class="memtemplate">
template&lt;typename KnotVectorType , typename ParameterVectorType , typename IndexArray &gt; </div>
      <table class="memname">
        <tr>
          <td class="memname">void Eigen::KnotAveragingWithDerivatives </td>
          <td>(</td>
          <td class="paramtype">const ParameterVectorType &amp;&#160;</td>
          <td class="paramname"><em>parameters</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const unsigned int&#160;</td>
          <td class="paramname"><em>degree</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const IndexArray &amp;&#160;</td>
          <td class="paramname"><em>derivativeIndices</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">KnotVectorType &amp;&#160;</td>
          <td class="paramname"><em>knots</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
      </table>
</div><div class="memdoc">

<p>Computes knot averages when derivative constraints are present. Note that this is a technical interpretation of the referenced article since the algorithm contained therein is incorrect as written. </p>
<dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramdir">[in]</td><td class="paramname">parameters</td><td>The parameters at which the interpolation B-Spline will intersect the given interpolation points. The parameters are assumed to be a non-decreasing sequence. </td></tr>
    <tr><td class="paramdir">[in]</td><td class="paramname">degree</td><td>The degree of the interpolating B-Spline. This must be greater than zero. </td></tr>
    <tr><td class="paramdir">[in]</td><td class="paramname">derivativeIndices</td><td>The indices corresponding to parameters at which there are derivative constraints. The indices are assumed to be a non-decreasing sequence. </td></tr>
    <tr><td class="paramdir">[out]</td><td class="paramname">knots</td><td>The calculated knot vector. These will be returned as a non-decreasing sequence</td></tr>
  </table>
  </dd>
</dl>
<dl class="section see"><dt>See also</dt><dd>Les A. Piegl, Khairan Rajab, Volha Smarodzinana. 2008. Curve interpolation with directional constraints for engineering design. Engineering with Computers </dd></dl>

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